The advancement of quantum optics has ushered in groundbreaking fields like quantum information and quantum control. While free-electron lasers have traditionally been studied through classical electromagnetism, this project, acronymed FELQO, seeks to explore the quantum nature of this system, aligning with the momentum of the second quantum revolution. By delving into the quantum optics of free-electron lasers, the project aims to achieve precise control over both electron wave functions and light fields, positioning this system as a versatile platform for quantum simulation and computing. In this innovative and interdisciplinary framework, the project will also tackle fundamental quantum challenges, including relativistic quantum dynamics and quantum measurement, which have intrigued scientists since the inception of quantum theory. This proposal represents a bold step into a novel and fundamental area of research, promising to deepen our understanding and potentially shape future quantum technologies.